Gravitation

Every object attracts every other object with a force directly proportional to product of masses and inversely proportional to square of distance. F = Gm₁m₂/r². G = 6.674×10⁻¹¹ N⋅m²/kg² (gravitational constant). This force acts along the line joining the two objects. It's always attractive, never repulsive.

1st Law (Law of Orbits): Planets move in elliptical orbits with Sun at one focus. 2nd Law (Law of Areas): Line joining planet to Sun sweeps equal areas in equal times (planet moves faster when closer to Sun). 3rd Law (Law of Periods): T² ∝ r³. Square of time period is proportional to cube of semi-major axis.

g = GM/R² (at Earth's surface). g = 9.8 m/s² at surface. Variation: g decreases as height increases (g_h = g(R/(R+h))²). g decreases inside Earth (g_d = g(1-d/R)). g is maximum at poles, minimum at equator (due to rotation and shape). g on Moon = g_Earth/6 ≈ 1.6 m/s².

Orbital velocity: minimum velocity for satellite to orbit (gravitational force = centripetal force): v_o = √(GM/r) = √(gR²/r). For orbit just above Earth: v_o ≈ 7.9 km/s. Escape velocity: minimum velocity to escape Earth's gravity: v_e = √(2GM/R) = √(2gR) ≈ 11.2 km/s = √2 × v_o.